If A = ( 1 2 2 3 ) and B = ( 1 1 0 0 ) then what is determinant of AB?, 0, 1, 10, 20

Let A = [ 1 2 2 3 ] and B = [ 1 1 0 0 ] AB = [ 1 2 2 3 ] [ 1 1 0 0 ] ⇒ AB = [ 3 5 0 0 ] So, ∣ AB ∣ = 0 ( ∵ one column is zero )

If A = ( 1 2 2 3 ) and B = ( 1 1 0 0 ) then what is determinant of AB?

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Question: Answered & Verified by Expert

If $\mathrm{A}=\left(\begin{array}{ll}1 & 2 \\ 2 & 3\end{array}\right)$ and $\mathrm{B}=\left(\begin{array}{ll}1 & 0 \\ 1 & 0\end{array}\right)$ then what is determinant of AB?

MathematicsDeterminantsNDANDA 2012 (Phase 1)

Options:

A 0
B 1
C 10
D 20

Solution:

1284 Upvotes Verified Answer

The correct answer is: 0

$\begin{array}{l}\text { Let } \mathrm{A}=\left[\begin{array}{ll}1 & 2 \\ 2 & 3\end{array}\right] \text { and } \mathrm{B}=\left[\begin{array}{ll}1 & 0 \\ 1 & 0\end{array}\right] \\ \mathrm{AB}=\left[\begin{array}{ll}1 & 2 \\ 2 & 3\end{array}\right]\left[\begin{array}{ll}1 & 0 \\ 1 & 0\end{array}\right] \Rightarrow \mathrm{AB}=\left[\begin{array}{ll}3 & 0 \\ 5 & 0\end{array}\right] \\ \text { So, }|\mathrm{AB}|=0 & (\because \text { one column is zero })\end{array}$

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